IMO 2019 Shortlist N4

Let Zą0 be the set of positive integers. A positive integer constant C is given. Find all functions f : Zą0 Ñ Zą0 such t...

imomathematicsolympiadshortlistnumber-theory

IMO 2019 Shortlist N4

Category: Number Theory

Problem

Let Zą0 be the set of positive integers. A positive integer constant C is given. Find all functions f : Zą0 Ñ Zą0 such that, for all positive integers a and b satisfying a b ą C, a fpbq | a2 ` bfpaq. (Croatia)